Question

If the compound interest on an amount of 29000 in two years is 9352.5, what is the rate of interest?
$\begin{gathered}
  A.11\% \\
  B.9\% \\
  C.15\% \\
  D.18\% \\
\end{gathered} $

Answer 1

Hint: Before attempting this question, one should have prior knowledge about the rate of interest and compound interest and also remember compound interest is the interest calculated on the initial principal including the interest from the previous periods on the deposit, use this information to approach the solution of the problem.
\[Amount = P{\left( {1 + \dfrac{R}{{100}}} \right)^n}\]

Complete step-by-step answer:
Given: Principle amount (P)= 29000, Compound Interest (C.I.) = 9352.5, time(n)= 2 years. Let the rate of interest be R. The amount after 2 years can be given by,
\[Amount = P{\left( {1 + \dfrac{R}{{100}}} \right)^n}\]
Putting all the value in the formula,
\[Amount = 29000{\left( {1 + \dfrac{R}{{100}}} \right)^2}\] (equation 1)
And amount = P + C.I.
= 29000 + 9352.5
= 38352.5
Putting in equation (1), we get
\[38352.5 = 29000{\left( {1 + \dfrac{R}{{100}}} \right)^2}\]
$ \Rightarrow $\[\dfrac{{38352.5}}{{29000}} = {\left( {1 + \dfrac{R}{{100}}} \right)^2}\]
$ \Rightarrow $\[{\left( {1 + \dfrac{R}{{100}}} \right)^2} = 1.3225\]
Taking square root both sides, we get
\[\left( {1 + \dfrac{R}{{100}}} \right) = \sqrt {1.3225} \]
$ \Rightarrow $\[\left( {1 + \dfrac{R}{{100}}} \right) = 1.15\]
$ \Rightarrow $\[\dfrac{R}{{100}} = 1.15 - 1\]
$ \Rightarrow $\[\dfrac{R}{{100}} = 0.15\]
$ \Rightarrow $\[R = 0.15 \times 100\]
$ \Rightarrow $R = 15%

So, the correct answer is “Option C”.

Note: In the above solution we came across the term “compound interest” which can be explained as the total interest to the loan or deposits principal sum or we can say that it is the reinvesting interest’s product, instead of paying it back, because interest on the principal sum plus previously accrued interest is then paid in the next cycle.